EFA-function
Tingying He, Petra Isenberg
3/23/2022
Summary
This markdown document contains the code and references for the exploratory factor analysis conducted as part of our VIS 2022 Paper submission on a Validated Scale for Aesthetic Pleasure in Visualization
References Considered
Recommendations Extracted From The Literature
Variables to Include
- at least 3 measured variables are need for statistical identification of a factor
- recommend 4 - 6 indicators per factor
- more indicators are preferable
Participants to Include
- some ratio of the number of variables to the number of factors such as 5:1 or 10:1 or some arbitrary number of participants such as 100 or 200
Distributional Properties of the Data
- Variability
- Linearity
- Normality: reverse negatviely variables
- Level of Measurement: methodologists have recommended that EFA be based on polychoric correlations if the ordinal variables are measured by fewer than five to seven categories or when distributions of the ordinal variables are asymmetrical
- Missing Data
- Outliers: Methods to detect outliers include boxplots and scatterplots for individual variables as well as Mahalanobis distance for multiple variables
Measurement Error
Fabrigar et al. (1999) recommended that variables with reliabilities below .70 should be avoided in EFA. However, adhering to this reliability standard may not be possible when analyzing test items.
#Preparation ## Loading Required Packages
library(png)
library(psych)
library(EFA.dimensions)
library(imager)## Loading required package: magrittr##
## Attaching package: 'imager'## The following object is masked from 'package:magrittr':
##
## add## The following objects are masked from 'package:stats':
##
## convolve, spectrum## The following object is masked from 'package:graphics':
##
## frame## The following object is masked from 'package:base':
##
## save.imagelibrary(corrplot)## corrplot 0.92 loadedlibrary(knitr)
library(kableExtra)
library(xtable)##
## Attaching package: 'xtable'## The following objects are masked from 'package:imager':
##
## display, labellibrary(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:kableExtra':
##
## group_rows## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(tibble)
library(ggplot2)##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alphaLoading Required Files
participantResponseFiles <- list.files(path= "./data",pattern = "\\.csv$") #names correspond to images, one participant per row, one word per column
imageFiles <- list.files(path= "./images",pattern = "\\.png$")Helper Methods
#Clean the column names
cleanColnames <- function(data){
newNames <- gsub("^.+?\\.(.+?)\\..*$", "\\1", colnames(data))
return(newNames)
}Methods Used in the Analysis
Methods to Test the Appropriateness of the Data for EFA
Correlation
“A subjective method is to examine the correlation matrix. A sizable number of correlations should exceed ±.30 or EFA may be inappropriate”
correlation <- function(num,data){
return(cor(data))
}Bartlett’s test of sphericity
An objective test of the factorability of the correlation matrix is Bartlett’s (1954) test of sphericity, which statistically tests the hypothesis that the correlation matrix contains ones on the diagonal and zeros on the off-diagonals. Hence, that it was generated by random data. This test should produce a statistically significant chi-square value to justify the application of EFA.
If the p-value from Bartlett’s Test of Sphericity is lower than our chosen significance level (common choices are 0.10, 0.05, and 0.01), then our dataset is suitable for a data reduction technique. (https://www.statology.org/bartletts-test-of-sphericity/)
bartlettTest <- function(num,data){
bart <- cortest.bartlett(correlation(num,data), n = nrow(data))
if(bart[2]>0.05) cat("WARNING the p value is above 0.05") else cat("The p value is below 0.05. We are good to continue.")
cat("\n\n")
print(bart)
return(bart)
}KMO
Large sample sizes make the Bartlett test sensitive to even trivial deviations from randomness, so its results should be supplemented with a measure of sampling adequacy. The Kaiser-Meyer-Olkin (KMO; Kaiser, 1974) measure of sampling adequacy is the ratio of correlations and partial correlations that reflects the extent to which correlations are a function of the variance shared across all variables rather than the variance shared by particular pairs of variables. KMO values range from 0.00 to 1.00 and can be computed for the total correlation matrix as well as for each measured variable.
- KMO values ≥.70 are desired
- KMO values ≤.50 are generally considered unacceptable
KMOTest <- function(num,data){
kmo <- KMO(data)
cat(paste("The overall measure of sampling adequacy is: ",kmo[1]))
cat("\n\n")
if(kmo[1]<.7) cat("WARNING the sampling adequacy has dropped below 0.7") else cat("The sampling adequacy is above 0.7. We are generally good.")
cat("\n\n")
return(kmo)
}The Number of Factors to Retain
Measurement specialists have conducted simulation studies and concluded that parallel analysis and MAP are the most accurate empirical estimates of the number of factors to retain and that scree is a useful subjective adjunct to the empirical estimates. Unfortunately, no method has been found to be correct in all situations, so it is necessary to employ multiple methods and carefully judge each plausible solution to identify the most appropriate factor solution.
parallelAnalysis <- function(num,data){
pdf(paste(paste("generatedPlots-EFA/ScreePlot-Image_",num,sep=""),'.pdf'), width=8, height=4)
parallel <- fa.parallel(correlation(num,data), n.obs=nrow(data), fa="fa", n.iter=100, main="Scree plots with parallel analysis")
dev.off()
cat("\n\n")
}EFA
Model of Factor Analysis
- two models: PCA, common factor analysis
- When the goal of research is to identify latent constructs for theory building or to create measurement instruments in which the researcher wishes to make the case that the resulting measurement instrument reflects a meaningful underlying construct, we argue that common factor analysis (EFA) procedures are usually preferable.
- this distinction may make little difference when there are ≥40 measured variables
Estimation Method
- two estimation methods: ML and PA
- Statistical simulations have found that PA outperforms ML when the relationships between measured variables and factors are relatively weak (≤.40), sample size is relatively small (≤300), multivariate normality is violated, or when the number of factors underlying the measured variables is misspecified
EFA <- function(num, factor, rotation,data){
efa <- fa(correlation(num,data), nfactors = factor, rotate = rotation, fm = "pa")
#print(xtable(unclass(efa$Structure)),type="html")
print(efa,sort=TRUE)
#fa.diagram(efa,cut=.4,digits=2) #I don't fint this diagram particularly useful
return(efa)
}Analyzing Participant Responses Per Image
analyze_image <-function(num){
#First we plot the image that we are analyzing first
image <- load.image(paste("images/",imageFiles[[num]],sep=""))
plot(image)
cat("\n\n")
data <- read.csv(paste("data/",participantResponseFiles[[num]],sep=""), encoding="UTF-8")
colnames(data) <- cleanColnames(data)
#Then we go through the analysis steps. These are explained in detail above
#1. Correlation
# cat("### Correlation\n")
# corr <- correlation(num,data)
# pdf(paste(paste("generatedPlots-EFA/CorrelationMatrix-Image_",num,sep=""),'.pdf'), width=8, height=4)
# corrplot(corr, method="square",tl.col="black",title=paste("Correlation for Image ",num),number.cex = 0.5)
# dev.off()
# cat("\n\n")
#
# cat("### Bartlett’s test of sphericity\n")
# bartlettTest(num,data)
# cat("\n\n")
#
# cat("### KMO\n")
# KMOTest(num,data)
# cat("\n\n")
cat("## Scree Plot and Parallel Analysis\n")
parallelAnalysis(num,data)
cat("\n\n")
cat("## Exploratory Factor Analysis - 1 Factor - No Rotation\n")
efa <- EFA(num, 1, "none",data)
cat("\n\n")
#
# #Exploratory Analyses below here
# cat("## Exploratory Factor Analysis - 2 Factors - Varimax Rotation(Orthogonal rotation)\n")
# EFA(num, 2, "varimax",data )
# cat("\n\n")
#
# cat("## Exploratory Factor Analysis - 2 Factors - Promax Rotation(Pblique rotation)\n")
# EFA(num, 2, "promax",data )
# cat("\n\n")
return(efa)
}imageCount <- length(participantResponseFiles)
#For debugging we can set the imageCount to whatever we want
#imageCount <- 1
df <- NULL
for (i in 1:imageCount){
cat(paste(paste("## Image ",i),"\n"))
efa <- analyze_image(i) #we want to create a big table with all the factor loadings so we'll save the efa results here
if(i == 1){
df <- as.data.frame(unclass(efa$loadings))
colnames(df) <- c(paste("PA1 Image ",i))
df <- tibble::rownames_to_column(df,"terms")
}
else{
dftemp <- as.data.frame(unclass(efa$loadings))
colnames(dftemp) <- c(paste("PA1 Image ",i))
dftemp <- tibble::rownames_to_column(dftemp,"terms")
df <- merge(df,dftemp,by="terms")
}
}## ## Image 1##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 2 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## likable 19 0.91 0.820 0.18 1
## nice 22 0.90 0.818 0.18 1
## enjoyable 13 0.87 0.764 0.24 1
## delightful 10 0.86 0.731 0.27 1
## pleasing 24 0.85 0.721 0.28 1
## appealing 1 0.85 0.719 0.28 1
## pretty 25 0.85 0.716 0.28 1
## lovely 20 0.85 0.716 0.28 1
## beautiful 5 0.84 0.707 0.29 1
## attractive 3 0.84 0.707 0.29 1
## elegant 11 0.83 0.696 0.30 1
## inviting 18 0.83 0.694 0.31 1
## exciting 14 0.79 0.625 0.38 1
## engaging 12 0.79 0.624 0.38 1
## harmonious 16 0.79 0.621 0.38 1
## tasteful 30 0.78 0.615 0.38 1
## satisfying 28 0.77 0.597 0.40 1
## wellDesigned 31 0.76 0.578 0.42 1
## motivating 21 0.74 0.549 0.45 1
## clean 6 0.73 0.527 0.47 1
## interesting 17 0.70 0.495 0.51 1
## balanced 4 0.69 0.480 0.52 1
## sophisticated 29 0.68 0.467 0.53 1
## fascinating 15 0.68 0.458 0.54 1
## colorHarmonious 8 0.65 0.427 0.57 1
## professional 26 0.63 0.400 0.60 1
## organized 23 0.59 0.348 0.65 1
## creative 9 0.53 0.284 0.72 1
## artistic 2 0.52 0.268 0.73 1
## cluttered 7 0.30 0.093 0.91 1
## provoking 27 0.17 0.029 0.97 1
##
## PA1
## SS loadings 17.29
## Proportion Var 0.56
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 29.91
## The degrees of freedom for the model are 434 and the objective function was 5.64
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.06
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.96
##
##
## ## Image 2##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 2 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## nice 22 0.81 0.653 0.35 1
## pleasing 24 0.80 0.646 0.35 1
## appealing 1 0.80 0.644 0.36 1
## likable 19 0.79 0.619 0.38 1
## enjoyable 13 0.78 0.609 0.39 1
## attractive 3 0.78 0.601 0.40 1
## beautiful 5 0.77 0.587 0.41 1
## elegant 11 0.76 0.572 0.43 1
## pretty 25 0.76 0.571 0.43 1
## lovely 20 0.75 0.560 0.44 1
## delightful 10 0.74 0.553 0.45 1
## inviting 18 0.74 0.541 0.46 1
## satisfying 28 0.73 0.540 0.46 1
## wellDesigned 31 0.71 0.499 0.50 1
## interesting 17 0.70 0.494 0.51 1
## engaging 12 0.70 0.490 0.51 1
## clean 6 0.70 0.484 0.52 1
## harmonious 16 0.69 0.477 0.52 1
## professional 26 0.67 0.450 0.55 1
## exciting 14 0.66 0.440 0.56 1
## motivating 21 0.65 0.424 0.58 1
## tasteful 30 0.64 0.414 0.59 1
## fascinating 15 0.64 0.413 0.59 1
## balanced 4 0.63 0.394 0.61 1
## sophisticated 29 0.63 0.391 0.61 1
## organized 23 0.61 0.378 0.62 1
## colorHarmonious 8 0.59 0.349 0.65 1
## artistic 2 0.49 0.241 0.76 1
## creative 9 0.49 0.240 0.76 1
## cluttered 7 -0.33 0.108 0.89 1
## provoking 27 0.20 0.039 0.96 1
##
## PA1
## SS loadings 14.42
## Proportion Var 0.47
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 23.71
## The degrees of freedom for the model are 434 and the objective function was 6.68
##
## The root mean square of the residuals (RMSR) is 0.09
## The df corrected root mean square of the residuals is 0.09
##
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.98
## Multiple R square of scores with factors 0.97
## Minimum correlation of possible factor scores 0.94
##
##
## ## Image 3##
##
## ## Scree Plot and Parallel Analysis## Parallel analysis suggests that the number of factors = 2 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## likable 19 0.88 0.770 0.23 1
## pleasing 24 0.84 0.699 0.30 1
## enjoyable 13 0.83 0.695 0.30 1
## attractive 3 0.81 0.658 0.34 1
## nice 22 0.81 0.651 0.35 1
## appealing 1 0.80 0.637 0.36 1
## lovely 20 0.78 0.602 0.40 1
## delightful 10 0.78 0.601 0.40 1
## pretty 25 0.77 0.599 0.40 1
## satisfying 28 0.77 0.590 0.41 1
## engaging 12 0.76 0.579 0.42 1
## harmonious 16 0.76 0.578 0.42 1
## beautiful 5 0.76 0.576 0.42 1
## fascinating 15 0.73 0.538 0.46 1
## exciting 14 0.72 0.526 0.47 1
## motivating 21 0.71 0.511 0.49 1
## inviting 18 0.71 0.509 0.49 1
## clean 6 0.71 0.507 0.49 1
## interesting 17 0.71 0.502 0.50 1
## elegant 11 0.71 0.500 0.50 1
## tasteful 30 0.68 0.466 0.53 1
## wellDesigned 31 0.67 0.446 0.55 1
## colorHarmonious 8 0.63 0.400 0.60 1
## sophisticated 29 0.62 0.387 0.61 1
## organized 23 0.62 0.384 0.62 1
## balanced 4 0.61 0.376 0.62 1
## creative 9 0.55 0.306 0.69 1
## professional 26 0.52 0.268 0.73 1
## artistic 2 0.51 0.259 0.74 1
## provoking 27 0.22 0.047 0.95 1
## cluttered 7 0.03 0.001 1.00 1
##
## PA1
## SS loadings 15.17
## Proportion Var 0.49
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 24.45
## The degrees of freedom for the model are 434 and the objective function was 5.55
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.07
##
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.97
## Minimum correlation of possible factor scores 0.95
##
##
## ## Image 4## Warning in readfun(f, ...): libpng warning: iCCP: known incorrect sRGB profile
##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 3 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## pleasing 24 0.88 0.774 0.23 1
## likable 19 0.87 0.752 0.25 1
## enjoyable 13 0.86 0.741 0.26 1
## delightful 10 0.85 0.716 0.28 1
## appealing 1 0.84 0.711 0.29 1
## satisfying 28 0.83 0.696 0.30 1
## nice 22 0.82 0.677 0.32 1
## lovely 20 0.82 0.670 0.33 1
## attractive 3 0.81 0.658 0.34 1
## beautiful 5 0.79 0.626 0.37 1
## pretty 25 0.78 0.607 0.39 1
## elegant 11 0.78 0.604 0.40 1
## wellDesigned 31 0.77 0.589 0.41 1
## fascinating 15 0.77 0.588 0.41 1
## motivating 21 0.77 0.587 0.41 1
## exciting 14 0.76 0.582 0.42 1
## harmonious 16 0.75 0.559 0.44 1
## engaging 12 0.74 0.553 0.45 1
## interesting 17 0.74 0.544 0.46 1
## organized 23 0.74 0.541 0.46 1
## balanced 4 0.73 0.539 0.46 1
## inviting 18 0.73 0.535 0.47 1
## tasteful 30 0.72 0.518 0.48 1
## clean 6 0.64 0.413 0.59 1
## sophisticated 29 0.63 0.403 0.60 1
## colorHarmonious 8 0.63 0.403 0.60 1
## professional 26 0.61 0.374 0.63 1
## creative 9 0.60 0.362 0.64 1
## artistic 2 0.59 0.347 0.65 1
## provoking 27 0.28 0.081 0.92 1
## cluttered 7 0.15 0.022 0.98 1
##
## PA1
## SS loadings 16.77
## Proportion Var 0.54
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 28.05
## The degrees of freedom for the model are 434 and the objective function was 5.73
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.06
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.96
##
##
## ## Image 5##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 2 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## pleasing 24 0.89 0.792 0.21 1
## nice 22 0.87 0.766 0.23 1
## appealing 1 0.87 0.750 0.25 1
## likable 19 0.86 0.746 0.25 1
## enjoyable 13 0.86 0.746 0.25 1
## attractive 3 0.86 0.743 0.26 1
## satisfying 28 0.85 0.725 0.28 1
## beautiful 5 0.84 0.698 0.30 1
## delightful 10 0.83 0.689 0.31 1
## motivating 21 0.83 0.685 0.31 1
## inviting 18 0.82 0.675 0.32 1
## harmonious 16 0.82 0.675 0.33 1
## exciting 14 0.81 0.663 0.34 1
## wellDesigned 31 0.81 0.657 0.34 1
## pretty 25 0.81 0.652 0.35 1
## lovely 20 0.80 0.637 0.36 1
## engaging 12 0.78 0.613 0.39 1
## tasteful 30 0.77 0.587 0.41 1
## interesting 17 0.76 0.577 0.42 1
## elegant 11 0.74 0.544 0.46 1
## balanced 4 0.71 0.510 0.49 1
## clean 6 0.70 0.489 0.51 1
## fascinating 15 0.70 0.486 0.51 1
## organized 23 0.67 0.454 0.55 1
## creative 9 0.67 0.450 0.55 1
## artistic 2 0.66 0.432 0.57 1
## colorHarmonious 8 0.64 0.405 0.59 1
## professional 26 0.62 0.382 0.62 1
## sophisticated 29 0.61 0.368 0.63 1
## cluttered 7 0.39 0.150 0.85 1
## provoking 27 0.28 0.079 0.92 1
##
## PA1
## SS loadings 17.83
## Proportion Var 0.58
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 30.56
## The degrees of freedom for the model are 434 and the objective function was 5.71
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.06
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.96
##
##
## ## Image 6##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 2 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## pleasing 24 0.87 0.763 0.24 1
## attractive 3 0.87 0.755 0.24 1
## likable 19 0.84 0.706 0.29 1
## enjoyable 13 0.84 0.702 0.30 1
## nice 22 0.83 0.687 0.31 1
## appealing 1 0.83 0.687 0.31 1
## delightful 10 0.81 0.658 0.34 1
## pretty 25 0.81 0.657 0.34 1
## satisfying 28 0.80 0.645 0.35 1
## inviting 18 0.80 0.639 0.36 1
## tasteful 30 0.78 0.611 0.39 1
## motivating 21 0.78 0.611 0.39 1
## engaging 12 0.78 0.604 0.40 1
## beautiful 5 0.78 0.601 0.40 1
## lovely 20 0.77 0.590 0.41 1
## exciting 14 0.76 0.574 0.43 1
## harmonious 16 0.74 0.554 0.45 1
## wellDesigned 31 0.73 0.534 0.47 1
## fascinating 15 0.72 0.519 0.48 1
## interesting 17 0.71 0.509 0.49 1
## balanced 4 0.69 0.483 0.52 1
## elegant 11 0.68 0.457 0.54 1
## colorHarmonious 8 0.63 0.395 0.60 1
## artistic 2 0.63 0.395 0.61 1
## sophisticated 29 0.62 0.390 0.61 1
## creative 9 0.62 0.386 0.61 1
## clean 6 0.60 0.363 0.64 1
## organized 23 0.59 0.345 0.65 1
## professional 26 0.53 0.282 0.72 1
## provoking 27 0.33 0.108 0.89 1
## cluttered 7 0.18 0.033 0.97 1
##
## PA1
## SS loadings 16.24
## Proportion Var 0.52
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 27.12
## The degrees of freedom for the model are 434 and the objective function was 5.91
##
## The root mean square of the residuals (RMSR) is 0.07
## The df corrected root mean square of the residuals is 0.07
##
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.95
##
##
## ## Image 7##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 3 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## satisfying 28 0.90 0.813 0.19 1
## likable 19 0.90 0.807 0.19 1
## pleasing 24 0.90 0.803 0.20 1
## attractive 3 0.89 0.795 0.20 1
## delightful 10 0.89 0.787 0.21 1
## enjoyable 13 0.88 0.781 0.22 1
## pretty 25 0.88 0.773 0.23 1
## appealing 1 0.88 0.767 0.23 1
## beautiful 5 0.87 0.761 0.24 1
## nice 22 0.87 0.760 0.24 1
## motivating 21 0.84 0.706 0.29 1
## inviting 18 0.84 0.703 0.30 1
## lovely 20 0.83 0.693 0.31 1
## elegant 11 0.83 0.691 0.31 1
## engaging 12 0.82 0.674 0.33 1
## exciting 14 0.81 0.657 0.34 1
## fascinating 15 0.80 0.647 0.35 1
## tasteful 30 0.80 0.642 0.36 1
## harmonious 16 0.74 0.550 0.45 1
## sophisticated 29 0.73 0.529 0.47 1
## interesting 17 0.73 0.527 0.47 1
## artistic 2 0.69 0.471 0.53 1
## wellDesigned 31 0.69 0.471 0.53 1
## clean 6 0.66 0.432 0.57 1
## creative 9 0.66 0.430 0.57 1
## professional 26 0.60 0.355 0.64 1
## balanced 4 0.59 0.344 0.66 1
## organized 23 0.55 0.304 0.70 1
## colorHarmonious 8 0.48 0.227 0.77 1
## cluttered 7 0.27 0.072 0.93 1
## provoking 27 0.19 0.037 0.96 1
##
## PA1
## SS loadings 18.01
## Proportion Var 0.58
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 33.25
## The degrees of freedom for the model are 434 and the objective function was 6.4
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.06
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.97
##
##
## ## Image 8##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 2 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## likable 19 0.88 0.77 0.23 1
## enjoyable 13 0.87 0.76 0.24 1
## nice 22 0.87 0.76 0.24 1
## inviting 18 0.85 0.72 0.28 1
## appealing 1 0.85 0.72 0.28 1
## pleasing 24 0.84 0.71 0.29 1
## attractive 3 0.84 0.70 0.30 1
## engaging 12 0.83 0.69 0.31 1
## delightful 10 0.82 0.67 0.33 1
## lovely 20 0.81 0.66 0.34 1
## beautiful 5 0.81 0.65 0.35 1
## tasteful 30 0.81 0.65 0.35 1
## satisfying 28 0.80 0.65 0.35 1
## pretty 25 0.79 0.63 0.37 1
## exciting 14 0.77 0.59 0.41 1
## motivating 21 0.75 0.56 0.44 1
## interesting 17 0.74 0.55 0.45 1
## harmonious 16 0.74 0.55 0.45 1
## fascinating 15 0.71 0.50 0.50 1
## wellDesigned 31 0.71 0.50 0.50 1
## balanced 4 0.70 0.49 0.51 1
## creative 9 0.70 0.48 0.52 1
## clean 6 0.70 0.48 0.52 1
## elegant 11 0.69 0.47 0.53 1
## sophisticated 29 0.65 0.43 0.57 1
## artistic 2 0.61 0.37 0.63 1
## organized 23 0.60 0.36 0.64 1
## colorHarmonious 8 0.55 0.30 0.70 1
## professional 26 0.46 0.21 0.79 1
## provoking 27 0.37 0.14 0.86 1
## cluttered 7 0.34 0.11 0.89 1
##
## PA1
## SS loadings 16.86
## Proportion Var 0.54
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 28.96
## The degrees of freedom for the model are 434 and the objective function was 6.18
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.07
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.96
##
##
## ## Image 9##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 3 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## appealing 1 0.85 0.72 0.28 1
## attractive 3 0.84 0.71 0.29 1
## enjoyable 13 0.84 0.71 0.29 1
## likable 19 0.84 0.71 0.29 1
## satisfying 28 0.82 0.68 0.32 1
## nice 22 0.81 0.66 0.34 1
## tasteful 30 0.81 0.65 0.35 1
## pleasing 24 0.80 0.65 0.35 1
## delightful 10 0.79 0.62 0.38 1
## inviting 18 0.78 0.61 0.39 1
## pretty 25 0.76 0.58 0.42 1
## beautiful 5 0.76 0.57 0.43 1
## motivating 21 0.75 0.56 0.44 1
## lovely 20 0.74 0.54 0.46 1
## engaging 12 0.74 0.54 0.46 1
## wellDesigned 31 0.73 0.53 0.47 1
## fascinating 15 0.72 0.51 0.49 1
## elegant 11 0.71 0.50 0.50 1
## exciting 14 0.70 0.49 0.51 1
## harmonious 16 0.69 0.48 0.52 1
## sophisticated 29 0.66 0.43 0.57 1
## balanced 4 0.65 0.42 0.58 1
## creative 9 0.62 0.39 0.61 1
## interesting 17 0.61 0.37 0.63 1
## clean 6 0.60 0.36 0.64 1
## organized 23 0.59 0.35 0.65 1
## artistic 2 0.56 0.32 0.68 1
## professional 26 0.50 0.25 0.75 1
## colorHarmonious 8 0.43 0.19 0.81 1
## cluttered 7 0.41 0.17 0.83 1
## provoking 27 0.32 0.10 0.90 1
##
## PA1
## SS loadings 15.38
## Proportion Var 0.50
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 25.71
## The degrees of freedom for the model are 434 and the objective function was 6.37
##
## The root mean square of the residuals (RMSR) is 0.07
## The df corrected root mean square of the residuals is 0.07
##
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.97
## Minimum correlation of possible factor scores 0.95
##
##
## ## Image 10##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 2 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## appealing 1 0.88 0.772 0.23 1
## pleasing 24 0.88 0.770 0.23 1
## enjoyable 13 0.87 0.755 0.25 1
## likable 19 0.86 0.736 0.26 1
## attractive 3 0.86 0.733 0.27 1
## nice 22 0.85 0.718 0.28 1
## satisfying 28 0.85 0.717 0.28 1
## elegant 11 0.84 0.707 0.29 1
## beautiful 5 0.82 0.678 0.32 1
## delightful 10 0.82 0.670 0.33 1
## lovely 20 0.81 0.661 0.34 1
## tasteful 30 0.80 0.642 0.36 1
## pretty 25 0.80 0.642 0.36 1
## harmonious 16 0.80 0.638 0.36 1
## inviting 18 0.78 0.613 0.39 1
## balanced 4 0.77 0.599 0.40 1
## motivating 21 0.77 0.595 0.40 1
## exciting 14 0.77 0.586 0.41 1
## engaging 12 0.76 0.578 0.42 1
## wellDesigned 31 0.74 0.546 0.45 1
## creative 9 0.68 0.464 0.54 1
## clean 6 0.68 0.458 0.54 1
## artistic 2 0.66 0.439 0.56 1
## fascinating 15 0.66 0.436 0.56 1
## organized 23 0.66 0.433 0.57 1
## interesting 17 0.64 0.412 0.59 1
## sophisticated 29 0.63 0.395 0.61 1
## colorHarmonious 8 0.62 0.379 0.62 1
## professional 26 0.61 0.375 0.62 1
## cluttered 7 0.45 0.199 0.80 1
## provoking 27 0.27 0.075 0.92 1
##
## PA1
## SS loadings 17.42
## Proportion Var 0.56
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 29.01
## The degrees of freedom for the model are 434 and the objective function was 5.16
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.06
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.96
##
##
## ## Image 11##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 2 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## pleasing 24 0.87 0.756 0.24 1
## delightful 10 0.86 0.738 0.26 1
## lovely 20 0.86 0.732 0.27 1
## satisfying 28 0.86 0.731 0.27 1
## enjoyable 13 0.85 0.728 0.27 1
## appealing 1 0.85 0.725 0.27 1
## likable 19 0.85 0.721 0.28 1
## beautiful 5 0.85 0.718 0.28 1
## attractive 3 0.85 0.715 0.29 1
## nice 22 0.84 0.708 0.29 1
## pretty 25 0.84 0.698 0.30 1
## inviting 18 0.83 0.696 0.30 1
## exciting 14 0.82 0.674 0.33 1
## tasteful 30 0.82 0.669 0.33 1
## engaging 12 0.79 0.630 0.37 1
## motivating 21 0.78 0.615 0.38 1
## harmonious 16 0.77 0.596 0.40 1
## wellDesigned 31 0.76 0.571 0.43 1
## elegant 11 0.76 0.571 0.43 1
## balanced 4 0.74 0.543 0.46 1
## fascinating 15 0.73 0.531 0.47 1
## clean 6 0.71 0.504 0.50 1
## interesting 17 0.70 0.490 0.51 1
## creative 9 0.65 0.424 0.58 1
## artistic 2 0.64 0.416 0.58 1
## organized 23 0.64 0.409 0.59 1
## sophisticated 29 0.63 0.398 0.60 1
## professional 26 0.52 0.273 0.73 1
## colorHarmonious 8 0.51 0.257 0.74 1
## provoking 27 0.40 0.162 0.84 1
## cluttered 7 0.21 0.043 0.96 1
##
## PA1
## SS loadings 17.44
## Proportion Var 0.56
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 30.52
## The degrees of freedom for the model are 434 and the objective function was 6.32
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.07
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.96
##
##
## ## Image 12##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 3 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## likable 19 0.89 0.7856 0.21 1
## pleasing 24 0.88 0.7768 0.22 1
## enjoyable 13 0.88 0.7728 0.23 1
## delightful 10 0.88 0.7665 0.23 1
## appealing 1 0.88 0.7658 0.23 1
## satisfying 28 0.87 0.7625 0.24 1
## attractive 3 0.87 0.7591 0.24 1
## lovely 20 0.86 0.7360 0.26 1
## beautiful 5 0.85 0.7302 0.27 1
## pretty 25 0.85 0.7196 0.28 1
## nice 22 0.82 0.6727 0.33 1
## wellDesigned 31 0.81 0.6639 0.34 1
## elegant 11 0.80 0.6454 0.35 1
## harmonious 16 0.80 0.6356 0.36 1
## inviting 18 0.78 0.6007 0.40 1
## fascinating 15 0.77 0.5983 0.40 1
## exciting 14 0.77 0.5939 0.41 1
## engaging 12 0.77 0.5864 0.41 1
## tasteful 30 0.76 0.5750 0.42 1
## sophisticated 29 0.75 0.5642 0.44 1
## interesting 17 0.73 0.5309 0.47 1
## motivating 21 0.71 0.5097 0.49 1
## clean 6 0.71 0.5007 0.50 1
## artistic 2 0.69 0.4813 0.52 1
## professional 26 0.67 0.4544 0.55 1
## balanced 4 0.66 0.4393 0.56 1
## organized 23 0.66 0.4316 0.57 1
## creative 9 0.64 0.4139 0.59 1
## colorHarmonious 8 0.62 0.3830 0.62 1
## provoking 27 0.32 0.1052 0.89 1
## cluttered 7 -0.05 0.0025 1.00 1
##
## PA1
## SS loadings 17.96
## Proportion Var 0.58
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 31.16
## The degrees of freedom for the model are 434 and the objective function was 5.62
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.06
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.96
##
##
## ## Image 13##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 2 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## nice 22 0.89 0.795 0.21 1
## delightful 10 0.89 0.792 0.21 1
## appealing 1 0.88 0.777 0.22 1
## likable 19 0.87 0.759 0.24 1
## pleasing 24 0.87 0.759 0.24 1
## attractive 3 0.86 0.732 0.27 1
## satisfying 28 0.85 0.729 0.27 1
## inviting 18 0.84 0.702 0.30 1
## enjoyable 13 0.83 0.696 0.30 1
## motivating 21 0.83 0.690 0.31 1
## lovely 20 0.83 0.683 0.32 1
## pretty 25 0.83 0.681 0.32 1
## tasteful 30 0.81 0.663 0.34 1
## wellDesigned 31 0.81 0.653 0.35 1
## engaging 12 0.80 0.646 0.35 1
## exciting 14 0.79 0.617 0.38 1
## elegant 11 0.78 0.616 0.38 1
## beautiful 5 0.78 0.615 0.38 1
## harmonious 16 0.76 0.582 0.42 1
## fascinating 15 0.76 0.576 0.42 1
## interesting 17 0.74 0.543 0.46 1
## sophisticated 29 0.71 0.503 0.50 1
## balanced 4 0.68 0.463 0.54 1
## professional 26 0.67 0.455 0.54 1
## organized 23 0.65 0.428 0.57 1
## clean 6 0.63 0.391 0.61 1
## creative 9 0.58 0.333 0.67 1
## artistic 2 0.55 0.304 0.70 1
## colorHarmonious 8 0.43 0.184 0.82 1
## provoking 27 0.22 0.049 0.95 1
## cluttered 7 0.12 0.015 0.99 1
##
## PA1
## SS loadings 17.43
## Proportion Var 0.56
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 30.41
## The degrees of freedom for the model are 434 and the objective function was 5.77
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.06
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.96
##
##
## ## Image 14##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 2 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## likable 19 0.87 0.7587 0.24 1
## pretty 25 0.86 0.7423 0.26 1
## enjoyable 13 0.85 0.7269 0.27 1
## pleasing 24 0.84 0.7137 0.29 1
## attractive 3 0.84 0.7086 0.29 1
## delightful 10 0.84 0.7038 0.30 1
## appealing 1 0.83 0.6810 0.32 1
## nice 22 0.82 0.6775 0.32 1
## beautiful 5 0.82 0.6655 0.33 1
## satisfying 28 0.81 0.6585 0.34 1
## lovely 20 0.79 0.6310 0.37 1
## tasteful 30 0.77 0.5945 0.41 1
## motivating 21 0.76 0.5810 0.42 1
## inviting 18 0.76 0.5741 0.43 1
## harmonious 16 0.75 0.5699 0.43 1
## exciting 14 0.75 0.5672 0.43 1
## elegant 11 0.74 0.5485 0.45 1
## engaging 12 0.73 0.5393 0.46 1
## clean 6 0.73 0.5376 0.46 1
## balanced 4 0.71 0.5081 0.49 1
## sophisticated 29 0.71 0.5031 0.50 1
## fascinating 15 0.70 0.4908 0.51 1
## wellDesigned 31 0.66 0.4296 0.57 1
## colorHarmonious 8 0.64 0.4133 0.59 1
## organized 23 0.62 0.3901 0.61 1
## professional 26 0.62 0.3845 0.62 1
## interesting 17 0.59 0.3440 0.66 1
## artistic 2 0.58 0.3351 0.66 1
## creative 9 0.54 0.2940 0.71 1
## provoking 27 0.22 0.0492 0.95 1
## cluttered 7 0.05 0.0021 1.00 1
##
## PA1
## SS loadings 16.32
## Proportion Var 0.53
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 27.59
## The degrees of freedom for the model are 434 and the objective function was 5.94
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.07
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.95
##
##
## ## Image 15##
##
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors = 2 and the number of components = NA
##
##
##
##
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method = pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation,
## fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## V PA1 h2 u2 com
## appealing 1 0.90 0.813 0.19 1
## nice 22 0.89 0.795 0.20 1
## likable 19 0.89 0.794 0.21 1
## enjoyable 13 0.89 0.789 0.21 1
## delightful 10 0.88 0.781 0.22 1
## pleasing 24 0.88 0.771 0.23 1
## pretty 25 0.85 0.726 0.27 1
## attractive 3 0.85 0.722 0.28 1
## satisfying 28 0.84 0.705 0.29 1
## beautiful 5 0.84 0.703 0.30 1
## inviting 18 0.83 0.687 0.31 1
## tasteful 30 0.83 0.684 0.32 1
## lovely 20 0.83 0.682 0.32 1
## harmonious 16 0.81 0.652 0.35 1
## engaging 12 0.80 0.647 0.35 1
## elegant 11 0.80 0.633 0.37 1
## exciting 14 0.79 0.622 0.38 1
## motivating 21 0.77 0.588 0.41 1
## wellDesigned 31 0.76 0.582 0.42 1
## interesting 17 0.74 0.543 0.46 1
## balanced 4 0.74 0.543 0.46 1
## fascinating 15 0.71 0.501 0.50 1
## sophisticated 29 0.71 0.500 0.50 1
## clean 6 0.67 0.449 0.55 1
## artistic 2 0.67 0.443 0.56 1
## organized 23 0.65 0.426 0.57 1
## creative 9 0.65 0.418 0.58 1
## colorHarmonious 8 0.64 0.406 0.59 1
## professional 26 0.60 0.355 0.64 1
## provoking 27 0.35 0.126 0.87 1
## cluttered 7 0.24 0.056 0.94 1
##
## PA1
## SS loadings 18.14
## Proportion Var 0.59
##
## Mean item complexity = 1
## Test of the hypothesis that 1 factor is sufficient.
##
## The degrees of freedom for the null model are 465 and the objective function was 32.44
## The degrees of freedom for the model are 434 and the objective function was 6.31
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.06
##
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## PA1
## Correlation of (regression) scores with factors 0.99
## Multiple R square of scores with factors 0.98
## Minimum correlation of possible factor scores 0.96Factor Loadings for all images from the chosen FA method
write.table(df,"generatedData-EFA/factorLoadings_all_images.tsv",row.names=FALSE,sep='\t')
print(xtable(df),type="html")| terms | PA1 Image 1 | PA1 Image 2 | PA1 Image 3 | PA1 Image 4 | PA1 Image 5 | PA1 Image 6 | PA1 Image 7 | PA1 Image 8 | PA1 Image 9 | PA1 Image 10 | PA1 Image 11 | PA1 Image 12 | PA1 Image 13 | PA1 Image 14 | PA1 Image 15 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | appealing | 0.85 | 0.80 | 0.80 | 0.84 | 0.87 | 0.83 | 0.88 | 0.85 | 0.85 | 0.88 | 0.85 | 0.88 | 0.88 | 0.83 | 0.90 |
| 2 | artistic | 0.52 | 0.49 | 0.51 | 0.59 | 0.66 | 0.63 | 0.69 | 0.61 | 0.56 | 0.66 | 0.64 | 0.69 | 0.55 | 0.58 | 0.67 |
| 3 | attractive | 0.84 | 0.78 | 0.81 | 0.81 | 0.86 | 0.87 | 0.89 | 0.84 | 0.84 | 0.86 | 0.85 | 0.87 | 0.86 | 0.84 | 0.85 |
| 4 | balanced | 0.69 | 0.63 | 0.61 | 0.73 | 0.71 | 0.69 | 0.59 | 0.70 | 0.65 | 0.77 | 0.74 | 0.66 | 0.68 | 0.71 | 0.74 |
| 5 | beautiful | 0.84 | 0.77 | 0.76 | 0.79 | 0.84 | 0.78 | 0.87 | 0.81 | 0.76 | 0.82 | 0.85 | 0.85 | 0.78 | 0.82 | 0.84 |
| 6 | clean | 0.73 | 0.70 | 0.71 | 0.64 | 0.70 | 0.60 | 0.66 | 0.70 | 0.60 | 0.68 | 0.71 | 0.71 | 0.63 | 0.73 | 0.67 |
| 7 | cluttered | 0.30 | -0.33 | 0.03 | 0.15 | 0.39 | 0.18 | 0.27 | 0.34 | 0.41 | 0.45 | 0.21 | -0.05 | 0.12 | 0.05 | 0.24 |
| 8 | colorHarmonious | 0.65 | 0.59 | 0.63 | 0.63 | 0.64 | 0.63 | 0.48 | 0.55 | 0.43 | 0.62 | 0.51 | 0.62 | 0.43 | 0.64 | 0.64 |
| 9 | creative | 0.53 | 0.49 | 0.55 | 0.60 | 0.67 | 0.62 | 0.66 | 0.70 | 0.62 | 0.68 | 0.65 | 0.64 | 0.58 | 0.54 | 0.65 |
| 10 | delightful | 0.86 | 0.74 | 0.78 | 0.85 | 0.83 | 0.81 | 0.89 | 0.82 | 0.79 | 0.82 | 0.86 | 0.88 | 0.89 | 0.84 | 0.88 |
| 11 | elegant | 0.83 | 0.76 | 0.71 | 0.78 | 0.74 | 0.68 | 0.83 | 0.69 | 0.71 | 0.84 | 0.76 | 0.80 | 0.78 | 0.74 | 0.80 |
| 12 | engaging | 0.79 | 0.70 | 0.76 | 0.74 | 0.78 | 0.78 | 0.82 | 0.83 | 0.74 | 0.76 | 0.79 | 0.77 | 0.80 | 0.73 | 0.80 |
| 13 | enjoyable | 0.87 | 0.78 | 0.83 | 0.86 | 0.86 | 0.84 | 0.88 | 0.87 | 0.84 | 0.87 | 0.85 | 0.88 | 0.83 | 0.85 | 0.89 |
| 14 | exciting | 0.79 | 0.66 | 0.72 | 0.76 | 0.81 | 0.76 | 0.81 | 0.77 | 0.70 | 0.77 | 0.82 | 0.77 | 0.79 | 0.75 | 0.79 |
| 15 | fascinating | 0.68 | 0.64 | 0.73 | 0.77 | 0.70 | 0.72 | 0.80 | 0.71 | 0.72 | 0.66 | 0.73 | 0.77 | 0.76 | 0.70 | 0.71 |
| 16 | harmonious | 0.79 | 0.69 | 0.76 | 0.75 | 0.82 | 0.74 | 0.74 | 0.74 | 0.69 | 0.80 | 0.77 | 0.80 | 0.76 | 0.75 | 0.81 |
| 17 | interesting | 0.70 | 0.70 | 0.71 | 0.74 | 0.76 | 0.71 | 0.73 | 0.74 | 0.61 | 0.64 | 0.70 | 0.73 | 0.74 | 0.59 | 0.74 |
| 18 | inviting | 0.83 | 0.74 | 0.71 | 0.73 | 0.82 | 0.80 | 0.84 | 0.85 | 0.78 | 0.78 | 0.83 | 0.78 | 0.84 | 0.76 | 0.83 |
| 19 | likable | 0.91 | 0.79 | 0.88 | 0.87 | 0.86 | 0.84 | 0.90 | 0.88 | 0.84 | 0.86 | 0.85 | 0.89 | 0.87 | 0.87 | 0.89 |
| 20 | lovely | 0.85 | 0.75 | 0.78 | 0.82 | 0.80 | 0.77 | 0.83 | 0.81 | 0.74 | 0.81 | 0.86 | 0.86 | 0.83 | 0.79 | 0.83 |
| 21 | motivating | 0.74 | 0.65 | 0.71 | 0.77 | 0.83 | 0.78 | 0.84 | 0.75 | 0.75 | 0.77 | 0.78 | 0.71 | 0.83 | 0.76 | 0.77 |
| 22 | nice | 0.90 | 0.81 | 0.81 | 0.82 | 0.87 | 0.83 | 0.87 | 0.87 | 0.81 | 0.85 | 0.84 | 0.82 | 0.89 | 0.82 | 0.89 |
| 23 | organized | 0.59 | 0.61 | 0.62 | 0.74 | 0.67 | 0.59 | 0.55 | 0.60 | 0.59 | 0.66 | 0.64 | 0.66 | 0.65 | 0.62 | 0.65 |
| 24 | pleasing | 0.85 | 0.80 | 0.84 | 0.88 | 0.89 | 0.87 | 0.90 | 0.84 | 0.80 | 0.88 | 0.87 | 0.88 | 0.87 | 0.84 | 0.88 |
| 25 | pretty | 0.85 | 0.76 | 0.77 | 0.78 | 0.81 | 0.81 | 0.88 | 0.79 | 0.76 | 0.80 | 0.84 | 0.85 | 0.83 | 0.86 | 0.85 |
| 26 | professional | 0.63 | 0.67 | 0.52 | 0.61 | 0.62 | 0.53 | 0.60 | 0.46 | 0.50 | 0.61 | 0.52 | 0.67 | 0.67 | 0.62 | 0.60 |
| 27 | provoking | 0.17 | 0.20 | 0.22 | 0.28 | 0.28 | 0.33 | 0.19 | 0.37 | 0.32 | 0.27 | 0.40 | 0.32 | 0.22 | 0.22 | 0.35 |
| 28 | satisfying | 0.77 | 0.73 | 0.77 | 0.83 | 0.85 | 0.80 | 0.90 | 0.80 | 0.82 | 0.85 | 0.86 | 0.87 | 0.85 | 0.81 | 0.84 |
| 29 | sophisticated | 0.68 | 0.63 | 0.62 | 0.63 | 0.61 | 0.62 | 0.73 | 0.65 | 0.66 | 0.63 | 0.63 | 0.75 | 0.71 | 0.71 | 0.71 |
| 30 | tasteful | 0.78 | 0.64 | 0.68 | 0.72 | 0.77 | 0.78 | 0.80 | 0.81 | 0.81 | 0.80 | 0.82 | 0.76 | 0.81 | 0.77 | 0.83 |
| 31 | wellDesigned | 0.76 | 0.71 | 0.67 | 0.77 | 0.81 | 0.73 | 0.69 | 0.71 | 0.73 | 0.74 | 0.76 | 0.81 | 0.81 | 0.66 | 0.76 |
Terms for which all factor loadings are >.7
remainingTerms <- df %>% filter_all(all_vars(. > 0.7))
write.table(remainingTerms,"generatedData-EFA/factorLoadingsAbove_.7_all_images.tsv",row.names=FALSE,sep='\t')
print(xtable(remainingTerms),type="html")| terms | PA1 Image 1 | PA1 Image 2 | PA1 Image 3 | PA1 Image 4 | PA1 Image 5 | PA1 Image 6 | PA1 Image 7 | PA1 Image 8 | PA1 Image 9 | PA1 Image 10 | PA1 Image 11 | PA1 Image 12 | PA1 Image 13 | PA1 Image 14 | PA1 Image 15 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | appealing | 0.85 | 0.80 | 0.80 | 0.84 | 0.87 | 0.83 | 0.88 | 0.85 | 0.85 | 0.88 | 0.85 | 0.88 | 0.88 | 0.83 | 0.90 |
| 2 | attractive | 0.84 | 0.78 | 0.81 | 0.81 | 0.86 | 0.87 | 0.89 | 0.84 | 0.84 | 0.86 | 0.85 | 0.87 | 0.86 | 0.84 | 0.85 |
| 3 | beautiful | 0.84 | 0.77 | 0.76 | 0.79 | 0.84 | 0.78 | 0.87 | 0.81 | 0.76 | 0.82 | 0.85 | 0.85 | 0.78 | 0.82 | 0.84 |
| 4 | delightful | 0.86 | 0.74 | 0.78 | 0.85 | 0.83 | 0.81 | 0.89 | 0.82 | 0.79 | 0.82 | 0.86 | 0.88 | 0.89 | 0.84 | 0.88 |
| 5 | enjoyable | 0.87 | 0.78 | 0.83 | 0.86 | 0.86 | 0.84 | 0.88 | 0.87 | 0.84 | 0.87 | 0.85 | 0.88 | 0.83 | 0.85 | 0.89 |
| 6 | inviting | 0.83 | 0.74 | 0.71 | 0.73 | 0.82 | 0.80 | 0.84 | 0.85 | 0.78 | 0.78 | 0.83 | 0.78 | 0.84 | 0.76 | 0.83 |
| 7 | likable | 0.91 | 0.79 | 0.88 | 0.87 | 0.86 | 0.84 | 0.90 | 0.88 | 0.84 | 0.86 | 0.85 | 0.89 | 0.87 | 0.87 | 0.89 |
| 8 | lovely | 0.85 | 0.75 | 0.78 | 0.82 | 0.80 | 0.77 | 0.83 | 0.81 | 0.74 | 0.81 | 0.86 | 0.86 | 0.83 | 0.79 | 0.83 |
| 9 | nice | 0.90 | 0.81 | 0.81 | 0.82 | 0.87 | 0.83 | 0.87 | 0.87 | 0.81 | 0.85 | 0.84 | 0.82 | 0.89 | 0.82 | 0.89 |
| 10 | pleasing | 0.85 | 0.80 | 0.84 | 0.88 | 0.89 | 0.87 | 0.90 | 0.84 | 0.80 | 0.88 | 0.87 | 0.88 | 0.87 | 0.84 | 0.88 |
| 11 | pretty | 0.85 | 0.76 | 0.77 | 0.78 | 0.81 | 0.81 | 0.88 | 0.79 | 0.76 | 0.80 | 0.84 | 0.85 | 0.83 | 0.86 | 0.85 |
| 12 | satisfying | 0.77 | 0.73 | 0.77 | 0.83 | 0.85 | 0.80 | 0.90 | 0.80 | 0.82 | 0.85 | 0.86 | 0.87 | 0.85 | 0.81 | 0.84 |